Linear light sources are used in a variety of applications. In particular, they are used in film scanners, to illuminate a line on the film. One type of linear light source being used in film scanners consists of a lamp and an integrating cavity of cylindrical shape and having a linear slot parallel to the cylindrical axis for emitting a line of diffuse light. Optical elements convey light from the lamp into the cavity through a port in the cavity. Inside the cavity, the light reflects off the interior surfaces, and exits through the linear slot in the cavity, providing a linear, uniform, diffuse source of light at the slot. Such a system is described in U.S. Pat. No. 4,868,383, issued Sep. 19, 1989 to Kurtz et al. The width of the exit slot in a film scanner for 35 mm film is generally on the order of 2-5 mm. In film scanner applications, the diffuseness of the light suppresses the undesirable optical effects of scratches in the film. However, while the cylindrical integrating cavity produces completely diffuse light, meaning the luminance is uniform at all angles up to 90.degree., only the light up to a certain angle (typically about 45.degree.) is useful in suppressing the scratch effects. The light beyond this angle is wasted, causing a loss of efficiency, and also possibly causing undesirable effects such as optical flare and heating of the film. There is a need therefore for a linear light source having means to limit the angular range of emitted light.